When a band-limited analog signal is digitally sampled with a sampling rate that is less than the minimum required rate for the exact reconstruction of the analog signal from its digital samples (the Nyquist rate), information loss occurs. This results in a degradation of signal quality when the digital signal is converted back to analog form. A method is desired that will let the user of an analog signal sampling device view in which parts of the analog signal information loss occurs (when a signal is sampled at a rate below the minimum rate required for maximum fidelity--i.e. by the Nyquist rate).
Information loss occurs at those time intervals of the analog signal which contain frequency components higher than half the sampling rate used. The Nyquist theorem states that in order to exactly reconstruct an analog signal from its digital samples, the sampling rate used must be greater than, or equal to, two times the maximum frequency component present in the band-limited signal. For example, if the maximum frequency component present in an analog signal is 250 kHz, then the signal must be sampled at a minimum of 500 kHz in order to be able to recover the signal from its samples without any information loss.
An analog signal X(t) (see FIG. 5) can be broken up into a summation of many "time-sliced" signals X.sub.i (t). Each time-slice of the signal can be treated as an individual analog signal to be sampled at the given sampling rate. The frequency contents of the time-slice can be obtained through a spectrum analyzer. If the maximum frequency present in a particular sample is greater than half of the rate used to sample the signal, then information loss has occurred for that sample or time-slice. A table in which each entry corresponds to a time-slice can be dynamically built by an analog to digital sampling device to identify those time intervals in which information loss has occurred. Another process can read the table and then display, in a user-friendly manner, where in the signal information loss occurred.
An audio signal defines such an analog signal. An audio signal, divided in time into a series of time-slices, may be thought of as a discreet series of "snap-shots" of the audio signal. Similarly, a video signal may be thought of as sampled into a discreet series of frames of the total signal. For any audio or video signal, only certain portions will experience information loss when the frequency content of a snap-shot of frame exceeds the Nyquist rate. Thus, there remains a need for a simple, user-friendly means of displaying to a user which snap-shot or frame experienced data loss in the digital sampling procedure. Further, such a system should provide additional means of illustrating how much of the analog signal was lost in a particular snap-shot or frame so that a determination can be made as to the acceptability of the degree of information loss.